Abstract The purpose of this competing continuation grant proposal is to continue developing, evaluating and applying methodological and statistical procedures to determine how prevention programs change outcome variables. These mediation analyses assess the link between program effects on the constructs targeted by a prevention program and effects on the outcome. As noted by many researchers, mediation analyses identify the most effective program components and increase understanding of the underlying processes leading to changing outcome variables. The P. I. of this grant received a one-year NIDA small grant and two four-year grants to develop and evaluate mediation analysis methods and statistical procedures for the designs and procedures commonly used in prevention research. The proposed five-year continuation study focuses on practical needs of researchers, applying recent statistical developments to mediation analysis, and developing methods for new prevention research designs. Four statistical topics represent the next steps in this research and will include analytical and simulation research as well as applications to actual etiological and prevention data. In Study 1, practical issues in significance testing are investigated including the best methods for studies with limited sample size and general methods to assess required sample size for any mediation design. Study 2 develops methods to assess how violations of assumptions of the mediation model lead to incorrect conclusions. Study 2 extends new developments in causal inference to mediation analysis to investigate and test assumptions of mediation analysis. Study 3 develops and evaluates longitudinal mediation methods beyond the latent growth curve modeling investigated in prior funding. Conceptual and statistical alternatives for mediation analysis of data from two waves and three or more waves will be thoroughly investigated. New alternative longitudinal mediation models based on autoregressive, latent difference, and exponential decay differential equation models will be developed and compared. Study 4 evaluates a general model developed in our prior research to investigate mediation when there are also moderator effects or program effects that differ by subgroups of participants. Moderator effects are common in prevention research. This study will also incorporate longitudinal relations in the general mediation and moderation model as well as investigate the types of effects common in prevention science. Study 5 applies the statistical methods to data from several NIH funded prevention data sets providing important feedback about the usefulness of the models. Study 6 disseminates new information about mediation analysis through our website, by communication with researchers, and publications from the project.